Precision measurement of a sub-nanometer order is demanded in various fields such as MEMS. A scanning probe microscope is used for such precision measurements. An atomic force microscope is known as a typical example of a scanning probe microscope.
The atomic force microscope has an oscillating cantilever. A probe is formed at the cantilever tip. The probe is influenced by an atomic force according to its distance from a measurement object. Equivalent stiffness of the cantilever is changed by this influence of the atomic force. The change in the equivalent stiffness appears as a change in the natural frequency of the cantilever. Therefore, if the change in the natural frequency of the cantilever is detected and the influence of the atomic force acting on the probe is calculated from the change in the natural frequency that is detected, it is possible to measure the distance between the probe and the measurement object. By scanning the measurement of the distance between the probe and the measurement object on the surface of the measurement object, the surface shape of the measurement object is measured in sub-nanometer order. The resolution of this measurement of a surface shape depends on the ease and accuracy of detection of the change in the natural frequency of the cantilever.
In a conventional atomic force microscope, an external excitation method for a cantilever is adopted.
The following two methods exist as methods for detecting a change in the natural frequency of a cantilever. The first is a method for detecting a change in the resonance frequency itself of the cantilever and calculating a change in the natural frequency from the detected change in the resonance frequency. A second method detects a decrease in the response amplitude with respect to a predetermined resonance frequency and calculates a change in the natural frequency from the decrease in the detected response amplitude.
In both methods, a Q value of an environment in which the cantilever is placed (the environment in which the cantilever is placed is hereinafter referred to as the “measurement environment”) affects the detection accuracy of a change in a natural frequency. The Q value is determined mainly by the viscous damping coefficient of the measurement environment. For example, the viscous damping coefficient is extremely small in vacuum; the Q value is large, and a resonance peak of the cantilever appears acutely. Consequently, in vacuum, it is possible to detect a change in a resonance frequency easily and accurately. Conversely, the viscous damping coefficient is large in a liquid; the Q value is small, and a resonance peak of the cantilever does not appear acutely even if the cantilever is forced to oscillate. It is therefore difficult to detect a change in a resonance frequency accurately in a liquid.
To address such problems imparted by the environment, a technique for oscillating a cantilever in a self-excited manner and controlling an actuator as an oscillation source attached to the cantilever according to feedback control of positive velocity feedback has been proposed recently (see Japanese Patent No. 3229914). FIG. 6 shows a block diagram of the feedback control in this self-excitation technique for a cantilever.
An atomic force microscope has a cantilever 10, a displacement detector 34, an oscillation velocity calculator 36, an amplifier 48, and an actuator 20.
The actuator 20, as an oscillation source, is connected to the cantilever 10. Self-excited oscillation is generated in the cantilever 10 driven by the actuator 20. A probe 12 is formed on the free end of the tip of the cantilever 10.
The displacement detector 34 is constituted to be capable of detecting an oscillation displacement x of the cantilever 10.
The oscillation velocity calculator 36 is a differentiator. The oscillation velocity calculator 36 is constituted to be capable of receiving x from the displacement detector 34, differentiating the received x, and calculating dx/dt as the oscillation velocity of cantilever 10.
The amplifier 48 is constituted to be capable of receiving dx/dt from the oscillation velocity calculator 36, multiplying the received dx/dt by a linear feedback gain K of a positive value to calculate K·dx/dt, and transmitting the calculated K·dx/dt to a driver 60 as a feedback control signal S1.
The driver 60 is constituted to be capable of amplifying the feedback control signal S1 received from the amplifier 48 and transmitting the feedback control signal S1 to the actuator 20.
The generated feedback control signal S1 is a feedback control signal of positive velocity feedback and is represented as the following Eq. (1).S1=K·dx/dt   (1)
The displacement detector 34 detects an oscillation displacement x of the cantilever 10. The feedback control signal S1 is generated from the detected x. Then this feedback control signal S1 is amplified by the driver 60 to drive the actuator 20; self-excited oscillation is generated in the cantilever 10.
As indicated by Eq. (1), the feedback control signal S1 changes linearly with a linear feedback gain K in association with a change in the oscillation velocity dx/dt of the cantilever 10. A response amplitude a of the cantilever 10 is represented by a function g in the following Eq. (2).a=g(K)   (2)
FIG. 7i shows a curve C of an amplitude characteristic of the cantilever 10 represented by Eq. (2). In FIG. 7i, the linear feedback gain K is plotted on the abscissa and the response amplitude a is plotted on the ordinate.
FIG. 7i shows that the response amplitude a is 0 and self-excited oscillation is not generated in the cantilever 10 when the linear feedback gain K is equal to or less than an oscillation critical value KLL1. When the linear feedback gain K is larger than the oscillation critical value KLL1, self-excited oscillation is generated in the cantilever 10 and, as the linear feedback gain K increases, the response amplitude a also increases. Under a condition of KLL1<K, when the linear feedback gain K is brought close to the oscillation critical value KLL1, the response amplitude a of the self-excitedly oscillating cantilever 10 decreases.
According to linear vibration theory, the oscillation frequency of the self-excited cantilever 10 is equal to its natural frequency. However, according to nonlinear vibration theory, as the oscillation amplitude of the cantilever 10 increases, the oscillation frequency of the cantilever 10 deviates from its natural frequency.
Limiting the response amplitude a of the cantilever 10 to a small value and preventing contact of the probe 12 of the cantilever 10 and the measurement object 70 is required for measurement. When the measurement object 70 is an object that is easily damaged such as an organism-related sample, if the probe 12 comes into contact with the measurement object 70, the measurement object 70 can be damaged easily by the probe 12. Therefore, the response amplitude a must be limited to be equal to or less than a fixed amplitude upper limit value aUL. The amplitude upper limit value aUL is the maximum value of the response amplitude a at which the contact of the measurement object 70 and the probe 12 is prevented. Curve C of the amplitude characteristic in FIG. 7i shows that the value KUL1 of the linear feedback gain K corresponding to the amplitude upper limit value aUL is a gain upper limit value.
That is, the actuator 20 is driven with the linear feedback gain K that satisfies the condition of KLL1<K≦KUL1; the self-excited oscillation of the cantilever 10 is maintained. At the same time, the response amplitude a is maintained as equal to or less than the amplitude upper limit value aUL. Consequently, contact of the probe 12 of the cantilever 10 and the measurement object 70 is prevented.